A fallacy is a misleading argument or belief based on a falsehood. If you oppose state testing in schools, you think it is a fallacy that educational quality can be measured by standardized tests.
Fallacy comes from the Latin fallacia, for deceit. It technically means a flaw in an argument that makes it deceptive or misleading. In poetry, the "pathetic fallacy" is the false idea that things like rocks or stars have human feelings (pathos). Fallacy can also be used more generally for any false statement or idea. Some synonyms are misconception and error.